If `sinx+cosx=sqrt(y+1/y)` for `x in [0,pi]` , then

Options

A. `x=pi/4`
B. `y=0`
C. `y=1`
D. `x=(3pi)/4`

Explanation

`sinx+cos=sqrt(y+1/y)`

`sqrt(2/3)(sinx+cosx)=sqrt((sqrty)^2+(1/sqrty)^2)`

`sqrt2(1/sqrt2sinx+1/sqrt2cosx)=sqrt((sqrty-1/sqrty)^2+2sqrty*1/sqrty)`

`sqrt2(sinpi/4sinx+sinpi/4cosx)=sqrt((sqrty-1/sqrty)^2+2`

`sqrt2sin(x+pi/4)=sqrt((sqrty-1/sqrty)^2+2`

LHS

`sqrt2sin(x+pi/4)`

`-1<=sin(x+pi/4)<=1`

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